Talk:Functional Just System
How to name a pythagorean interval
Implementing FJS naming is easy modulo getting to know names of pythagorean (3-limit) intervals. When I attempted to implement the latter, I ended up misnaming many intervals I picked for testing. I then went to see how the author of FJS solved that and came to this lovely function. That looks complicated, of a flavor “okay I can certainly walk this through, but what is the semantics of all these things?”. Though now, when seeing that the pythagorean d2 = [19 -12⟩ is descending, I think I understand what I have done wrong (at least I nailed P/M/m/A/d/AA/dd/… right! — but those are easy to see). But if you have a simpler, higher-level description of the naming schema, I would greatly appreciate that! --Arseniiv (talk) 22:52, 28 November 2020 (UTC)
- I'm not sure is this is what you are asking for but remember that I was highly confused by this naming scheme. The letters are secondary but come first. Pi = Perfect interval, Mi = major interval, mi = minor interval, Ai = Augmented interval, di = diminished interval, AAi = double augmented interval, ddi = double diminished interval. The intervals i are just numbered 1=unison, 2=second, 3=third, 4=forth, etc. hope that helps --Xenwolf (talk) 23:58, 28 November 2020 (UTC)
- I have to admit that I have issues with the FJS in terms of how it handles intervals in the 2.3.11 subgroup, which is part of why I'm going through the effort of naming these other intervals with Alpharabian tuning. That said, I myself could use some help from anyone who was involved in the SHEFKHED naming system... --Aura (talk) 00:09, 29 November 2020 (UTC)
- I recently read that page too! I think FloraC even suggested another tolerance radius to rename some intervals. Aura maybe that one will work better for your vision of 2.3.11 intervals too? As of SHEFKHED, that one looks interesting and maybe I would take myself up to trying to implement it, but as at first glance it’s indeed very sophisticated, and as it also names only edostep intervals, that may prove being hard to do. If I’ll end up with some algorithm sounding simpler than at SHEFKHED interval names, I’ll let you know! --Arseniiv (talk) 15:04, 29 November 2020 (UTC)
- I fixed my algorithm, now it correctly names 2048/2187 as d1, 2187/1024 as A8, 1073741824/1162261467 as dd2, 531441/262144 as A7, 2/3 as P−5 etc.. My troubles were with correctly calculating octave shift: at first I just took [math]\displaystyle{ \lfloor \log_2 \mathrm{interval} \rfloor }[/math], but that’s wrong because Cb is still the same octave as C, but one octave lower with this definition, and B# would be determined as one octave higher. Now it all works, though I need to make one part look nicer. --Arseniiv (talk) 15:04, 29 November 2020 (UTC)